I'm not sure which model Kwikee step you have and which Parent Co. manufactured them. I would bet if you have a Kwikee step by Kwikee, that switch is unnecessary for the function you're asking about, If it is a Kwikee by Power Gear, it should be the same. I don't know anything about the Kwikee by Lippert.
If your steps are installed properly and we have to start there, no switch is necessary unless you, like me store you RV between trips with the steps up. If you read the normal operating sequences of your steps, there is what is called "last out feature". When you stop, turn off the ignition and open your door, the steps should extend and STAY extended even when you shut the door.
If your steps do not work in the manner described in the Installation and Operation Manual, follow the troubleshooting guide to find your problem. Here is a link for Manual
#888 look at Figures 10 and 11. #10 is with the override switch and #11 is without a override switch.
Now for your question regarding how the power is supplied, power comes from two sources, your coach batteries and your chassis battery. Only some long lost engineering spec tells the actual pick up point for the power. Figure out how your steps are wired, like Fig. 10 or 11 that is important in functioning and trouble shooting.
Just remember that the override switch "Bypasses the controller" it makes the steps extend and retract every time the door is opened or closed. Refer to the paragraph above regarding the "Last Out Function".
"I travel not to go anywhere, but to go. I travel for travel's sake. The great affair is to go". R. L. Stevenson
David Bishop
2002 Winnebago Adventurer 32V
2009 GMC Canyon
Roadmaster 5000
BrakeBuddy Classic II